Trajectories connecting two submanifolds on a non-complete
Lorentzian manifold

Rossella Bartolo, Anna Germinario, & Miguel Sanchez
Abstract:
This article presents existence and multiplicity results for orthogonal
trajectories joining two submanifolds
and
of a static space-time manifold
under the action of gravitational
and electromagnetic vector potential. The main technical difficulties
are because
may not be complete and
,
may not
be compact. Hence, a suitable convexity assumption and hypotheses
at infinity are needed. These assumptions are widely discussed in terms
of the electric and magnetic vector fields naturally associated.
Then, these vector fields become relevant from both their physical
interpretation and the mathematical gauge invariance of the equation
of the trajectories.